I am working with a complex scalar field written in terms of two independent real scalar fields and trying to derive the commutator relations.(adsbygoogle = window.adsbygoogle || []).push({});

So,

[tex] \phi = \frac{1}{\sqrt{2}} \left(\phi_1 + i \phi_2) [/tex]

where [itex]\phi_1[/itex] and [itex]\phi_2[/itex] are real.

When deriving,

[tex] [\phi(\vec{x},t),\dot{\phi}(\vec{x}',t)] = 0 [/tex]

I get terms like the following:

[tex][\phi_1(\vec{x},t),\dot{\phi}_2(\vec{x}',t)][/tex]

which I need to vanish. It makes sense to me that they should vanish, but how do I show this?

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# Complex Scalar Field in Terms of Two Independent Real Fields

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